Algebra-1

Question Analysis
This question tests the student's ability to solve a system of linear and quadratic equations algebraically. The system consists of a quadratic equation and a linear equation. The goal is to find the intersection points, if any, of the parabola and the line.

Key Concept Explanation
To solve the system, we substitute the linear equation into the quadratic equation to eliminate and form a single quadratic equation in . We then solve this quadratic equation for and substitute the values back into the linear equation to find the corresponding -values.

Step-by-step Solution
1. Substitute into the quadratic equation :

2. Rearrange the equation to standard form:

3. Solve the quadratic equation using the quadratic formula :

So,

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